A: When you are diluting a solution, the only thing you are adding to your stock solution is water.  Therefore, the amount of solute never changes.  The amount of solute is measured in moles.  Remember that the units for  Molarity are moles solute/liters solution

M x V = (moles/liter) x liters = MOLES!!

So, M₁V₁  = moles of solute

M₂V₂ also = moles of solute

The moles of solute doesn't change.  Therefore M₁V₁=M₂V₂

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